https://file.aiquickdraw.com/mathbot/file/1726686949841xoazlvo7.jpg

The image shows a question asking for the area of a trapezoidal figure on a grid. The given solution is \( 146 \, \text{square units} \). To ensure understanding, let me explain how to find the area of this trapezoid based on the image.

### Steps to find the area of a trapezoid:
1. **Formula**: The area \( A \) of a trapezoid can be calculated using:
   \[
   A = \frac{1}{2} \times (b_1 + b_2) \times h
   \]
   where:
   - \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (bases),
   - \( h \) is the height (the perpendicular distance between the parallel sides).

2. **Grid interpretation**:
   - Count the squares along the top base (\( b_1 \)).
   - Count the squares along the bottom base (\( b_2 \)).
   - Measure the height by counting the squares vertically between the two parallel sides.

From the image:
- Top base \( b_1 \approx 8 \) units.
- Bottom base \( b_2 \approx 14 \) units.
- Height \( h \approx 12 \) units.

### Calculation:
Using the trapezoid area formula:
\[
A = \frac{1}{2} \times (8 + 14) \times 12 = \frac{1}{2} \times 22 \times 12 = 11 \times 12 = 132 \, \text{square units}.
\]

This differs slightly from the answer provided in the problem \( 146 \, \text{square units} \), which suggests there may be some rounding or a small discrepancy in the grid interpretation.

Would you like further details or clarification on this? Here are five related questions to expand your understanding:

1. How do you calculate the area of a trapezoid with decimal or fractional base lengths?
2. How do you handle irregular shapes or trapezoids with slanted sides in a grid?
3. What is the difference between calculating the area of a trapezoid and a parallelogram?
4. Can you apply the trapezoid area formula to a 3D shape (like a trapezoidal prism)?
5. How can you derive the trapezoid area formula from simpler geometric shapes?

**Tip**: When dealing with geometric figures on grids, be sure to carefully count the grid units, especially if the figure’s sides don’t perfectly align with the grid lines.

What is the area of the trapezoid shown on the grid?

Learn how to calculate the area of a trapezoid on a grid using the trapezoid area formula. This example uses grid counting to determine the base lengths and height. Perfect for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation